1. (6 points) In lecture, examples were shown on how to calculate the points of operating curves assuming the lot size, N, is finite. For this exercise, assume N is infinite. Suppose now that a quality engineer samples 50 units from an infinite lot size and the engineer would like to calculate a point of the operating characteristic curve for an acceptance number 2. Calculate the point at which the lot proportion of defectives, p, equals 0.06. 2. (5 points) Consider a process with an upper spec limit of 180 grams, a lower spec limit of 170 grams, and a mean of 176 grams. A. If the standard deviation is 1.2 grams, is the process "capable"? B. If the standard deviation is 1.5 grams, is the process "capable"? 3. (7 points) Consider a firm with a plant in the U.S. and the U.K. A U.S.-based shipper charges $2.50 per unit to ship between the two countries. Assume no taxes, and consider the following data. Weekly Demand Weekly Capacity Sales Price Production Cost U.S. 14,000 19,000 $43.00 $20.00 U.K. 9,000 15,000 22.00 10.60 A. Suppose that the exchange rate is 1.00 = $1.85. What is the best production distribution plan? B. Given your plan in part A, what is the profit in each country (expressed in dollars)